What is the integral of (3x-2)^7 ?

The integral of (3x-2)^7 is 1/24 (3x-2)^8+C

Popular >

integral of (3x-2)^7

\int (3 x - 2)^{7} d x

\frac{1}{24} (3 x - 2)^{8} + C

Solution steps

\int (3 x - 2)^{7} d x

Apply u-substitution

: \int \frac{u ^{7}}{3} d u

= \int \frac{u ^{7}}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= \frac{1}{3} \cdot \frac{u ^{8}}{8}

Substitute back

u = 3 x - 2

= \frac{1}{3} \cdot \frac{( 3 x - 2 ) ^{8}}{8}

Simplify

\frac{1}{3} \cdot \frac{( 3 x - 2 ) ^{8}}{8} : \frac{1}{24} (3 x - 2)^{8}

= \frac{1}{24} (3 x - 2)^{8}

Add a constant to the solution

= \frac{1}{24} (3 x - 2)^{8} + C

\int cos^{2} (x) e^{x} d x

\int \frac{1}{( x ^{2} + 1 ) ( x + 2 ) ( x + 3 )} d x

\int \frac{( a ^{x} - b ^{x} )}{a ^{x} b ^{x}} d x

\int \frac{x ^{2} + 11 x}{( x - 1 ) ( x + 1 ) ^{2}} d x

\int \frac{1}{( x ^{2} - 4 x + 4 ) ( x ^{2} - 4 x + 5 )} d x